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E2 contributions to backward (e,e′) cross sections in heavy deformed nuclei
hog.
Parr. Nucl. Phys., Vol. 34, pp. 319-320, 1995 Copyright 0 1995 Elsevier Science Ltd tinted in Great Britain. All rights reserved 0146-6410/95
$29.00
0146-6410(95)00027-5
E2 Contributions to Backward (e,e’) Cross Sections in Heavy Deformed Nuclei* M. DINGFELDER,
and A. FAESSLER
R. NOJAROV
Inslirutfiir Theoretische Physik Universitd’t Tiibingen, Auf der Morgenstelle 14, D-72076 Tiibingen, Germany
ABSTRACT It is shown that E2 transitions to the rotational band of low lying Ml excitations in heavy deformed nuclei contribute to the Ml (e,e’) cross section at backward angles even at low incident energies of 50 MeV. The agreement after taking
with experiment
is improved
the E2 contributions
considerably,
especially
for intermediate
transferred
momenta,
into account.
KEYWORDS Ml and E2 excitations,
deformed
nuclei,
backward
inelastic
electron
scattering,
cross sections,
DWBA,
QRPA Low lying magnetic interest (Bohle
dipole
since their discovery et. al., 1984).
(Ml)
excitations
in deformed
in 1984 in Darmstadt
They are described
test for this models than the Ml
and interpreted
strength
distribution
sensitive to details of the nuclear structure. angles (usually
8 =
while the electric scattering.
165”)
favouring
inelastic
by various theoretical alone are the (e,e’)
and theoretical
electron
models.
scattering
A more stringent
cross sections,
which
The (e,e’) cross sections are measured at backward
transverse
ones are dominated
nuclei are of both experimental
by high precision backward
Magnetic
transitions.
by their longitudinal
On the other hand, their large longitudinal
transitions
part and therefore
often
are purely neglected
part could give rise to appreciable
are very scattering
transverse in backward
contributions
to
the cross sections. Another
fact is the observation
sections of heavy deformed
of systematic
nuclei.
deviations
There the theoretical
decrease faster at larger momentum
transfer
p as found experimentally.
in lighter
nuclei suggests to take possible contributions
transition
to the Z”Z< = 2+1
Z”Zi
=
1+1.
transition,
The
state
E2-excitation
of the rotational
energy
because of the large moment
between theory
is only of inertia.
30-50
built
with the energy resolution
keV larger than
= l+ states, we use a quasipartice mean field
tial. * van
The
It includes pairing correlations supported Hadronen
by the
und
Deutsche
part
consists
random-phase
of an axially
symmetric
in the BCS approximation.
Forschungsgemeinschaft
that
(DFG)
Kernen”
319
and
experimentally
E2 with
Ml
(Bohle
This energy separation
(e,e’) experiments. approximation deformed
The separable the
an accompanying
of the corresponding
Ml transition.
of the present high precision
et. a/.,
1994b).
arising from
up on top of the Ml excitation
Such a 2+ state was identified
To describe these Zi”
l+ excitations
The absence of these discrepancies
into account, band,
et. a/., 1985) in lsfiGd It lies only 21 keV higher than the strongest is comparable
in the Ml cross
and experiment
Ml form factors of low lying orbital
Graduiertenkolleg
(QRPA)
Woods-Saxon
residual interaction “Struktur
und
(Nojarov potenincludes
Wechselwirkung
M. Dingfelder et al.
320 1o-4 BI’I’
1'1'
I’I’I’I’I’ -Ml
+ E2
1o-5
1o-6
10.’
1o+
d
1
I
’
10
’
’
20
30
’
’
’
40
’
60
incident energy Fig. 1.
Total
DWBA
cross sections
versus the incident an compared quadrupole
and spin parts.
and isovector
channels.
of rotational
The relative
/CR remains a free parameter.
The Ml
resonance
w
(IVGQR),
&K=I(r)
and Blok,
h’IC h
IS
and ,17&,~=r (r),
(longitudinal)
The transition
densities are reduced matrix
are calculated
microscopically
1. It is seen that
the E2 cross section
in distorted
isoscalar
by the deformaby the condition
and its coupling
position
constant
of the isovector
(Nojarov
of the multipole
giant
Ml strength.
wave Born approximation (r) and the E2 transition
~~I,K=I
(transversal)
violated
microscopically invariant
the high lying orbital
density
for the strongest
Ml
(DWBA) densities
et. al., 1994a)
charge and current
excitation
is two orders of magnitude
the Ml cross section
with
shifts the theoretical
cross sections to higher transferred
and theoretical
in 156Gd
type and contains
symmetry
is rotational
with
becomes comparable experimental
transitions
excitation
operators.
They
using the QRPA wave functions.
Ml and E2 cross sections
The calculated
elements
Ml
is of Pyatov
by the experimental
separately
J&,Ii=l(~)
’
100
E2 and Ml+E2
Its is determined
1983) using the Ml transition
90
et. a/.,1984)
interaction
connected
are calculated
for Ml,
interaction
constant
isovector
’ ’
’
60
for the strongest
restores the rotational
It can be determined
and E2 cross sections
(Heisenberg
(Bohle
The quadrupole-quadrupole
The isoscalar coupling
invariance.
quadrupole
to experiment
’
’
70
[MeV]
165’)
energy, calculated
The isoscalar interaction
tion of the mean field.
(6 =
’
I ’
’
50
Ml cross sections
cross section and a very good agreement
already
at &ncidenr momenta.
are removed
with experiment
in 156Gd are shown
smaller
at low incident
= 50 MeV.
in figure
energies,
In this way the discrepancies
after adding
but
The higher multipolarity
the E2 contribution
between
to the Ml
is achieved.
REFERENCES Bohle
D., A. Richter, Phys.
Lett.
W. Steffen,
B, 137,
Bohle D., A. Richter,
A.E.L.
Dieperink,
N. Lo ludice,
F. Palumbo
and 0. Scholten
K. Heyde,
and A. Sevrin (1985).
P. Van Isacker, J. Moreau
Phys.
Rev. Lett., 55,
1661. Heisenberg
(1984).
27.
J. and H.P. Blok (1983).
Ann. Rev. Nucl. Part.
Nojarov
R., A. Faessler and M. Dingfelder
(1994a).
J. Phys.
Nojarov
R., A. Faessler and M. Dingfelder
(1994b).
Phys.
Sci., 33, 569. G: NucI.
Part. Phys., 20, Llll.
Rev. C, submitted.
Parr. Nucl. Phys., Vol. 34, pp. 319-320, 1995 Copyright 0 1995 Elsevier Science Ltd tinted in Great Britain. All rights reserved 0146-6410/95
$29.00
0146-6410(95)00027-5
E2 Contributions to Backward (e,e’) Cross Sections in Heavy Deformed Nuclei* M. DINGFELDER,
and A. FAESSLER
R. NOJAROV
Inslirutfiir Theoretische Physik Universitd’t Tiibingen, Auf der Morgenstelle 14, D-72076 Tiibingen, Germany
ABSTRACT It is shown that E2 transitions to the rotational band of low lying Ml excitations in heavy deformed nuclei contribute to the Ml (e,e’) cross section at backward angles even at low incident energies of 50 MeV. The agreement after taking
with experiment
is improved
the E2 contributions
considerably,
especially
for intermediate
transferred
momenta,
into account.
KEYWORDS Ml and E2 excitations,
deformed
nuclei,
backward
inelastic
electron
scattering,
cross sections,
DWBA,
QRPA Low lying magnetic interest (Bohle
dipole
since their discovery et. al., 1984).
(Ml)
excitations
in deformed
in 1984 in Darmstadt
They are described
test for this models than the Ml
and interpreted
strength
distribution
sensitive to details of the nuclear structure. angles (usually
8 =
while the electric scattering.
165”)
favouring
inelastic
by various theoretical alone are the (e,e’)
and theoretical
electron
models.
scattering
A more stringent
cross sections,
which
The (e,e’) cross sections are measured at backward
transverse
ones are dominated
nuclei are of both experimental
by high precision backward
Magnetic
transitions.
by their longitudinal
On the other hand, their large longitudinal
transitions
part and therefore
often
are purely neglected
part could give rise to appreciable
are very scattering
transverse in backward
contributions
to
the cross sections. Another
fact is the observation
sections of heavy deformed
of systematic
nuclei.
deviations
There the theoretical
decrease faster at larger momentum
transfer
p as found experimentally.
in lighter
nuclei suggests to take possible contributions
transition
to the Z”Z< = 2+1
Z”Zi
=
1+1.
transition,
The
state
E2-excitation
of the rotational
energy
because of the large moment
between theory
is only of inertia.
30-50
built
with the energy resolution
keV larger than
= l+ states, we use a quasipartice mean field
tial. * van
The
It includes pairing correlations supported Hadronen
by the
und
Deutsche
part
consists
random-phase
of an axially
symmetric
in the BCS approximation.
Forschungsgemeinschaft
that
(DFG)
Kernen”
319
and
experimentally
E2 with
Ml
(Bohle
This energy separation
(e,e’) experiments. approximation deformed
The separable the
an accompanying
of the corresponding
Ml transition.
of the present high precision
et. a/.,
1994b).
arising from
up on top of the Ml excitation
Such a 2+ state was identified
To describe these Zi”
l+ excitations
The absence of these discrepancies
into account, band,
et. a/., 1985) in lsfiGd It lies only 21 keV higher than the strongest is comparable
in the Ml cross
and experiment
Ml form factors of low lying orbital
Graduiertenkolleg
(QRPA)
Woods-Saxon
residual interaction “Struktur
und
(Nojarov potenincludes
Wechselwirkung
M. Dingfelder et al.
320 1o-4 BI’I’
1'1'
I’I’I’I’I’ -Ml
+ E2
1o-5
1o-6
10.’
1o+
d
1
I
’
10
’
’
20
30
’
’
’
40
’
60
incident energy Fig. 1.
Total
DWBA
cross sections
versus the incident an compared quadrupole
and spin parts.
and isovector
channels.
of rotational
The relative
/CR remains a free parameter.
The Ml
resonance
w
(IVGQR),
&K=I(r)
and Blok,
h’IC h
IS
and ,17&,~=r (r),
(longitudinal)
The transition
densities are reduced matrix
are calculated
microscopically
1. It is seen that
the E2 cross section
in distorted
isoscalar
by the deformaby the condition
and its coupling
position
constant
of the isovector
(Nojarov
of the multipole
giant
Ml strength.
wave Born approximation (r) and the E2 transition
~~I,K=I
(transversal)
violated
microscopically invariant
the high lying orbital
density
for the strongest
Ml
(DWBA) densities
et. al., 1994a)
charge and current
excitation
is two orders of magnitude
the Ml cross section
with
shifts the theoretical
cross sections to higher transferred
and theoretical
in 156Gd
type and contains
symmetry
is rotational
with
becomes comparable experimental
transitions
excitation
operators.
They
using the QRPA wave functions.
Ml and E2 cross sections
The calculated
elements
Ml
is of Pyatov
by the experimental
separately
J&,Ii=l(~)
’
100
E2 and Ml+E2
Its is determined
1983) using the Ml transition
90
et. a/.,1984)
interaction
connected
are calculated
for Ml,
interaction
constant
isovector
’ ’
’
60
for the strongest
restores the rotational
It can be determined
and E2 cross sections
(Heisenberg
(Bohle
The quadrupole-quadrupole
The isoscalar coupling
invariance.
quadrupole
to experiment
’
’
70
[MeV]
165’)
energy, calculated
The isoscalar interaction
tion of the mean field.
(6 =
’
I ’
’
50
Ml cross sections
cross section and a very good agreement
already
at &ncidenr momenta.
are removed
with experiment
in 156Gd are shown
smaller
at low incident
= 50 MeV.
in figure
energies,
In this way the discrepancies
after adding
but
The higher multipolarity
the E2 contribution
between
to the Ml
is achieved.
REFERENCES Bohle
D., A. Richter, Phys.
Lett.
W. Steffen,
B, 137,
Bohle D., A. Richter,
A.E.L.
Dieperink,
N. Lo ludice,
F. Palumbo
and 0. Scholten
K. Heyde,
and A. Sevrin (1985).
P. Van Isacker, J. Moreau
Phys.
Rev. Lett., 55,
1661. Heisenberg
(1984).
27.
J. and H.P. Blok (1983).
Ann. Rev. Nucl. Part.
Nojarov
R., A. Faessler and M. Dingfelder
(1994a).
J. Phys.
Nojarov
R., A. Faessler and M. Dingfelder
(1994b).
Phys.
Sci., 33, 569. G: NucI.
Part. Phys., 20, Llll.
Rev. C, submitted.